Dynamics of the human alpha rhythm: evidence for non-linearity?

OBJECT: For a better understanding of the physiological mechanisms responsible for alpha rhythms it is important to know whether non-linear processes play a role in their generation. We used non-linear forecasting in combination with surrogate data testing to investigate the prevalence and nature of alpha rhythm non-linearity, based on EEG recordings from humans. We interpreted these findings using computer simulations of the alpha rhythm model of Lopes da Silva et al. (1974). METHODS: EEGs were recorded at 02 and O1 in 60 healthy subjects (30 males; 30 females; age: 49.28 years; range 11-84) during a resting eyes-closed state. Four artefact-free epochs (2.5 s; sample frequency 200 Hz) from each subject were tested for non-linearity using a non-linear prediction statistic and phase-randomized surrogate data. A similar type of analysis was done on the output of the alpha model for different values of input. RESULTS: In the 480 (60 subjects, 2 derivations, 4 blocks) epochs studied, the null hypothesis that the alpha rhythms can result from linearly filtered noise, could be rejected in 6 cases (1.25%). The alpha model showed a bifurcation from a point attractor to a limit cycle at an input pulse density of 615 pps. Non-linearity could only be detected in the model output close to and beyond this bifurcation point. The sources of the non-linearity are the sigmoidal relationships between average membrane potential and output pulse density of the various cells of the neuronal populations. CONCLUSION: The alpha rhythm is a heterogeneous entity dynamically: 98.75% of the epochs (type I alpha) cannot be distinguished from filtered noise. Apparently, during these epochs the activity of the brain has such a high complexity that it cannot be distinguished from a random process. In 1.25% of the epochs (type II alpha) non-linearity was found which may be explained by dynamics in the vicinity of a bifurcation to a limit cycle. There is thus experimental evidence from the point of view of dynamics for the existence of the two types of alpha rhythm and the bifurcation predicted by the model.     

Bifurcation and control in a neural network with small and large delays

This paper investigates a neural network modeled by a scalar delay differential equation. The focus is placed upon the Hopf bifurcation generated by varying the interaction parameter. A general expression for the periodic solutions arising from the Hopf bifurcation is obtained, and the direction of the bifurcation is also determined. Then, our results are tested in the two limits of small and large delays. For small delays, it is shown that a Hopf bifurcation to sinusoidal oscillations emerges as long as the interaction parameter is large enough (bifurcation from infinity) (Rosenblat & Davis, 1979). For large delays, it is pointed out that the oscillation progressively changes from sine to square-wave (Chow et al., 1992, Hale and Huang, 1994). Moreover, a time delayed feedback control algorithm is introduced to generate the Hopf bifurcation at a desired bifurcation point for our neural network model. It is shown that the linear gain regulates the onset of the bifurcation, while the nonlinear gains govern the direction and the stability of the periodic solutions generated from the Hopf bifurcation.     

Pulse-type hardware chaotic neuron model and its bifurcation phenomena

A number of studies has recently been made on hardware for a biological neuron for application to information processing functions of neural networks. A model of a single neuron with chaotic dynamics (called “the chaotic neuron model” proposed by Aihara) has the following properties of biological neurons: graded responses, relative refractoriness, and spatio-temporal summation of inputs. The model exhibits not only periodic responses but also chaotic responses for periodic stimulation. It is suggested that, with the chaotic neuron model, new information processing structures can be realized in neural networks. Accordingly, a single-neuron model should be designed so as to have the properties of biological neurons. But a pulse-type hardware chaotic neuron model has not been found. We previously proposed a pulse-type hardware neuron model composed of a negative resistance circuit, resistors, and capacitors. We reported also that the pulse-type hardware neuron model exhibited continuous firing for a constant stimulus current. But chaotic features of the neuron model have not been investigated. In this paper, we show, firstly, that the pulse-type hardware neuron model has the features of the chaotic neuron model, and we show that it is useful for the pulse-type hardware chaotic neuron model. Next, we show that the pulse-type hardware chaotic neuron model has three chaotic regions in the bifurcation diagram to periodic pulse train stimulation, and we clarify the bifurcation route and the return map in each chaotic region.     

Characteristics of period adding bifurcation without chaos in firing pattern transitions in an experimental neural pacemaker

Time variant signals received by a neuron were encoded into and output in the changing firing patterns. Recent investigations revealed that the firing patterns changed according to certain bifurcation principles. Thus, the bifurcation scenarios among various firing patterns were fundamental to the study of neural coding. In this study one of the previous theoretically proposed scenarios, period adding bifurcation without chaos, was experimentally confirmed to exist in real neuronal activities. The realistic bifurcation process possessed integer multiple patterns not found in previous theoretical reports. The observed bifurcation process was simulated in the stochastic neuronal model and the generation of the integer multiple patterns were related to the interplay between the internal noise and the dynamics of the neuron.     

Protein Folding in the 2D Hydrophobic–Hydrophilic (HP) Square Lattice Model is Chaotic

Among the unsolved problems in computational biology, protein folding is one of the most interesting challenges. To study this folding, tools like neural networks and genetic algorithms have received a lot of attention, mainly due to the NP completeness of the folding process. The background idea that has given rise to the use of these algorithms is obviously that the folding process is predictable. However, this important assumption is disputable as chaotic properties of such a process have been recently highlighted. In this paper, which is an extension of a former work accepted to the 2011 International Joint Conference on Neural Networks (IJCNN11), the topological behavior of a well-known dynamical system used for protein folding prediction is evaluated. It is mathematically established that the folding dynamics in the 2D hydrophobic?Chydrophilic (HP) square lattice model, simply called the 2D model in this document, is indeed a chaotic dynamical system as defined by Devaney. Furthermore, the chaotic behavior of this model is qualitatively and quantitatively deepened, by studying other mathematical properties of disorder, namely: the indecomposability, instability, strong transitivity, and constants of expansivity and sensitivity. Some consequences for both biological paradigms and structure prediction using this model are then discussed. In particular, it is shown that some neural networks seems to be unable to predict the evolution of this model with accuracy, due to its complex behavior.     

Bifurcation analysis on a two-neuron system with distributed delays in the frequency domain.

In this paper, a general two-neuron model with distributed delays and a strong kernel is investigated. By applying the frequency domain approach and analyzing the associated characteristic equation, the existence of bifurcation parameter for the model is determined. Furthermore, if the mean delay used as a bifurcation parameter, it is found that Hopf bifurcation occurs for the strong kernel. This means that a family of periodic solutions bifurcates from the equilibrium when the bifurcation parameter exceeds a critical value. The direction and stability of the bifurcating periodic solutions are determined by the Nyquist criterion and the graphical Hopf bifurcation theorem. Some numerical simulations are given to justify the theoretical analysis results.     

Axonal bifurcation in the dorsal root ganglion of the cat: a light and electron microscopic study

Bifurcation of the axon of unipolar neurons in the dorsal root ganglion of the cat has been studied by light and electron microscopy. Osmic acid, Golgi and silver preparations have revealed two types of bifurcation: (1) of myelinated fibers characterized by constriction at the nodal region with peripheral and central branches of equal diameter; (2) of small fibers characterized by a broad triangular expansion at the junctional region with a much thicker peripheral as compared to the central branch. These differences in bifurcation of unmyelinated and myelinated axons can be related to the velocity of conduction in the peripheral nerve and dorsal roots. The ultrastructure of the nodal region at the bifurcation resembles the node of Ranvier of a peripheral nerve fiber. The node of Ranvier at the bifurcation consists of three cells of Schwann and adjacent cells are closely apposed and interdigitated. Neurofilaments and microtubules are prominent structures within the axoplasm at the nodal regions. They group into two streams as the unipolar process bifurcates, entering the peripheral and central branch respectively. At the junctional region within the axoplasm, numerous mitochondria and scattered multivesicular bodies are always observed.     

Identification and characterization of novel properties of the human D3 dopamine receptor

Among dopamine receptors, the function and properties of the D3 receptor subtype are poorly understood. Here we report the identification and characterization of two unique properties of the human D3 receptor. The D3 receptor exhibits a tolerance property wherein the magnitude of the second agonist-induced response is reduced by 60% compared to the first response and progressively decreases upon repeated agonist application. In addition, unlike the D2 dopamine receptor, the D3 receptor response terminates 15-fold more slowly upon agonist removal. Using D3/D2S chimeric receptors, we demonstrate that D3 receptor tolerance property is mediated by a novel conformational mechanism involving the D3 receptor second cytoplasmic region. The slow response termination rate property requires the third cytoplasmic region and is due to the high affinity of the D3 receptor for ligand as well as its unique G-protein signaling mechanism.     

Dopamine receptor pharmacology: interactions with serotonin receptors and significance for the aetiology and treatment of schizophrenia

The classification of dopamine receptors proposed more than two decades ago remains valid today. Based on biochemical and pharmaceutical properties two main classes of dopamine receptors can be distinguished: D(1)-like (D(1), D(5)) and D(2)-like (D(2), D(3), and D(4)) dopamine receptors. Dopamine receptors belong to the class of G protein-coupled receptors and signal to a wide range of membrane bound and intracellular effectors such as ion channels, secondary messenger systems and enzymes. Although the pharmacological properties of ligands for D(1)-like and D(2)-like dopamine receptors are quite different, the number of selective ligands for each of the five receptors subtypes is rather small. Many drugs used to treat neurological and neuropsychiatric disorders like Parkinson's disease, restless leg syndrome and schizophrenia have affinities for dopamine receptors. Such medications are not without limitations so the development of novel (selective or aselective) dopamine receptor ligands is of the utmost importance for improved therapeutic approaches for these diseases. In that respect it is also important to understand how dopamine receptor ligands affect receptor signalling processes such as desensitization, receptor heterodimerization and agonist-receptor trafficking, issues which will be discussed in the present review. Furthermore, attention is paid to interactions of dopamine receptors with serotonin receptors since many drugs used to treat above mentioned disorders of the brain also possess affinities for serotonin receptors. Because of the enormity of this area we have tried to focus more specifically on interactions within the prefrontal cortex where it appears that the serotonergic modulation of dopaminergic function might be very relevant to schizophrenia.     

The recalling process dynamics of associative memory neural networks in macrodynamical approach

The results of a computer study of the continuous-time version of macrodynamical system of equations governing the recalling process of associative memory neural networks are presented. The comparative analysis of two models of associative memory network—recurrent (autoassociative) and layered (feedforward)—is given. The phase portraits of macrodynamical system at a variety of representative values of parameter , the loading ratio, are obtained and the appearance of the bifurcation of equilibrium frustration (the saddle-node bifurcation) is demonstrated. The behavior of the basins of attraction of network dynamics equilibria is studied as well.     

A 4D approach to the analysis of functional brain images: application to FMRI data.

This paper presents a new approach to functional magnetic resonance imaging (FMRI) data analysis. The main difference lies in the view of what comprises an observation. Here we treat the data from one scanning session (comprising t volumes, say) as one observation. This is contrary to the conventional way of looking at the data where each session is treated as t different observations. Thus instead of viewing the v voxels comprising the 3D volume of the brain as the variables, we suggest the usage of the vt hypervoxels comprising the 4D volume of the brain-over-session as the variables. A linear model is fitted to the 4D volumes originating from different sessions. Parameter estimation and hypothesis testing in this model can be performed with standard techniques. The hypothesis testing generates 4D statistical images (SIs) to which any relevant test statistic can be applied. In this paper we describe two test statistics, one voxel based and one cluster based, that can be used to test a range of hypotheses. There are several benefits in treating the data from each session as one observation, two of which are: (i) the temporal characteristics of the signal can be investigated without an explicit model for the blood oxygenation level dependent (BOLD) contrast response function, and (ii) the observations (sessions) can be assumed to be independent and hence inference on the 4D SI can be made by nonparametric or Monte Carlo methods. The suggested 4D approach is applied to FMRI data and is shown to accurately detect the expected signal.     

大脑中动脉分叉角度与分叉处动脉瘤形成关系的研究

目的 探讨大脑中动脉(MCA)分叉角度与分叉处动脉瘤的关系.方法 选取成像质量较好的单侧MCA分叉处动脉瘤病人19例,应用3D-DSA造影获取三维图像,通过Philips三维工作站重建后获取患侧与健侧大脑中动脉分叉角度并进行同源配对t检验.结果 患侧MCA分叉角度与健侧MCA分叉角度的差别具有统计学显著性差异(P=0.00 ＜0.05).结论 MCA分叉处,分叉角度和动脉瘤的形成具有一定的关系.     

An optimal state estimation model of sensory integration in human postural balance

We propose a model for human postural balance, combining state feedback control with optimal state estimation. State estimation uses an internal model of body and sensor dynamics to process sensor information and determine body orientation. Three sensory modalities are modeled: joint proprioception, vestibular organs in the inner ear, and vision. These are mated with a two degree-of-freedom model of body dynamics in the sagittal plane. Linear quadratic optimal control is used to design state feedback and estimation gains. Nine free parameters define the control objective and the signal-to-noise ratios of the sensors. The model predicts statistical properties of human sway in terms of covariance of ankle and hip motion. These predictions are compared with normal human responses to alterations in sensory conditions. With a single parameter set, the model successfully reproduces the general nature of postural motion as a function of sensory environment. Parameter variations reveal that the model is highly robust under normal sensory conditions, but not when two or more sensors are inaccurate. This behavior is similar to that of normal human subjects. We propose that age-related sensory changes may be modeled with decreased signal-to-noise ratios, and compare the model's behavior with degraded sensors against experimental measurements from older adults. We also examine removal of the model's vestibular sense, which leads to instability similar to that observed in bilateral vestibular loss subjects. The model may be useful for predicting which sensors are most critical for balance, and how much they can deteriorate before posture becomes unstable.     

Bifurcation Properties for Fractional Order Delayed BAM Neural Networks

In the past several decades, many papers involving the stability and Hopf bifurcation of delayed neural networks have been published. However, the results on the stability and Hopf bifurcation for fractional order neural networks with delays and fractional order neural networks with leakage delays are very rare. This paper is concerned with the stability and the existence of Hopf bifurcation of fractional order BAM neural networks with or without leakage delay. The Laplace transform, stability and bifurcation theory of fractional-order differential equations and Matlab software will be applied. The stability condition and the sufficient criterion of existence of Hopf bifurcation for fractional order BAM neural networks with delay (leakage delay) are established. It is found that when the sum of two delays (leakage delay) crosses a critical value, then a Hopf bifurcation will appear. The obtained results play an important role in designing neural networks. Also the derived results are new and enrich the bifurcation theory of fractional order delayed differential equations.

     

A mathematical model for the formation of cerebral aneurysms

Cerebral aneurysms are hypothesized to be acquired lesions resulting from a loss of static equilibrium in the apical region of the bifurcation, which causes the opening angle of the bifurcation to change during the cardiac cycle. Repeated dynamic cycling may disrupt wall elements in a manner analogous to a wire breaking with repeated bending and result in the formation of an aneurysm. A mathematical model that predicts the geometry of arterial bifurcations is proposed. The model predicts that the transmural pressure in the larger branch is greater than or equal to that in the smaller branch and that the larger branch makes a smaller angle with the direction of the parent artery [corrected]. Bifurcations with smaller area ratios (the sum of the luminal areas of the branches divided by the luminal area of the parent artery) have smaller opening angles. When the area ratio is 1.0, the opening angle is about 90 degrees. The model concludes that the opening angle is constant during the cardiac cycle if the fractional change in the radii of the daughter and parent arteries is the same for any increase in blood pressure and if the ratio of transmural pressures in the parent and daughter branches does not change during the cardiac cycle. Otherwise, the bifurcation is considered predisposed to the development of an aneurysm.     

An acute experimental model of saccular aneurysms in the rat

A new and reproducible saccular aneurysm model has been developed at the bifurcation of the common carotid artery in rats. The details of the experimental methods and results are described. It is strongly suggested that the internal elastic lamina is a critical layer in saccular aneurysm formation, because an experimental saccular aneurysm can be produced immediately by transluminally damaging the inside of the arterial wall at the bifurcation of the common carotid artery. This saccular aneurysm model has several advantages: (i) it can be induced quickly and the success rate approaches 100% in rats; (ii) this technique can produce satisfactory experimental saccular aneurysms for other aneurysm studies, and in the future it will also be possible to use this technique to produce experimental saccular aneurysms in cerebral arteries of large animals.     

Milestones of neuronal development in the adult hippocampus

Adult hippocampal neurogenesis originates from precursor cells in the adult dentate gyrus and results in new granule cell neurons. We propose a model of the development that takes place between these two fixed points and identify several developmental milestones. From a presumably bipotent radial-glia-like stem cell (type-1 cell) with astrocytic properties, development progresses over at least two stages of amplifying lineage-determined progenitor cells (type-2 and type-3 cells) to early postmitotic and to mature neurons. The selection process, during which new neurons are recruited into function, and other regulatory influences differentially affect the different stages of development.     

An acute experimental model of saccular aneurysms in the rat

A new and reproducible saccular aneurysm model has been developed at the bifurcation of the common carotid artery in rats. The details of the experimental methods and results are described. It is strongly suggested that the internal elastic lamina is a critical layer in saccular aneurysm formation, because an experimental saccular aneurysm can be produced immediately by transluminally damaging the inside of the arterial wall at the bifurcation of the common carotid artery. This saccular aneurysm model has several advantages: (i) it can be induced quickly and the success rate approaches 100% in rats; (ii) this technique can produce satisfactory experimental saccular aneurysms for other aneurysm studies, and in the future it will also be possible to use this technique to produce experimental saccular aneurysms in cerebral arteries of large animals.     

Bifurcation and Oscillations of a Multi-ring Coupling Neural Network with Discrete Delays

It is well known that brain neural networks are composed of hundreds of millions of neurons with complicated connections. It is noteworthy that there are a large number of neural circuits formed by the coupling relationship in neural networks. However, the vast majority of existing studies on ring-structured networks were restricted to models with fewer neurons or single-ring structure. Here, we design a multi-ring coupling network model, which includes a large number of neurons and multiple rings, to simulate the brain network with multiple neural circuits, and use bifurcation theory to investigate the dynamic behavior of bifurcations and oscillations of the proposed model. Instead of the traditional method, the Coates flow graph method is used to derive explicit expressions for the higher-order determinants of the model. Then, the stability and Hopf bifurcation of the model are studied with the sum of discrete delays of each ring as the bifurcation parameter, and the explicit formula for its critical value is deduced. Our results suggest that in some cases, the stability of the model gradually deteriorates with increasing time delay and eventually destabilizes the system at some critical value. More specifically, the development of the instability (increasing time delay) leads to limit cycle and periodic oscillations, and the amplitude and period of the system are also affected by it.

     

Different degrees of loss of function between GEFS+ and SMEI Nav 1.1 missense mutants at the same residue induced by rescuable folding defects

Generalized epilepsy with febrile seizures plus (GEFS+) and severe myoclonic epilepsy of infancy (SMEI) differ in their clinical severity and prognosis even though mutations of the Na(v) 1.1 sodium channel are responsible for both disorders. We compared the electrophysiologic properties of two mutant Na(v) 1.1 channels characterized by distinct amino acid substitutions at the same residue position: GEFS+ (A1685V) and SMEI (A1685D). Both the mutants showed complete loss of function when expressed alone. However, the function of A1685V can be partly rescued by the β(1) subunit, consistently with a folding defect, whereas that of A1685D was not rescued. These electrophysiologic differences are consistent with the divergence in clinical severity between GEFS+ and SMEI.